The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1 X^3  1  1  1  1 X^2+X  1  1  X X^3+X^2+X  1 X^3+X  1  1 X^3+X^2 X^2  1  1 X^3 X^2  1  1  1  1  1  1  X  1  1 X^3  1  1  1 X^3+X^2+X  1  0  1  1 X^3 X^2 X^2 X^3+X^2 X^3+X^2  X X^3 X^2  0 X^2+X X^3+X X^3+X X^3+X^2+X X^3+X X^3+X  X X^3+X  0  1  1  1  1  1  1  1  1  1 X^2  1 X^3+X^2+X  1  1  1  1  X  1 X^2 X^3+X^2+X X^2  1  1  1
 0  1  1 X^2 X+1  1  X X^2+X+1  1  X  1 X^2+X+1 X+1 X^2+1 X^3  1  1 X^3+X^2  1  1 X^3+X  1 X^3+X X^3+X^2+1  1  1 X^3+X+1 X^2  1  1 X^3 X^3+X^2+1 X^3+X^2+X X^2+X+1 X^3+X^2+X+1 X^3  1 X^3+X^2+X X^3+X^2+1  1 X^3+X^2+X X^3+1 X^2  1  1  1 X^3+X^2+X X+1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  X  0 X^3  0  0  0 X^3 X^3+X X^3+X X^3+X^2+X  1  X  1 X^2+X X^3+X^2 X^3 X^2  X X^3+X  X  1  1 X^3+X^2+1 X^2 X^3+1
 0  0  X X^3+X X^3 X^3+X X^3+X  X X^3+X^2 X^2 X^3+X X^3+X^2 X^2+X X^2+X X^2 X^3 X^3+X^2 X^2+X X^2+X X^3+X  0 X^2 X^2+X X^3  0  X X^3+X^2 X^2 X^3+X^2 X^3+X^2+X X^3+X  X X^3 X^3+X^2+X  0 X^3+X^2+X X^3 X^2 X^3+X^2 X^2 X^3+X^2+X X^3+X^2+X X^3 X^2+X  0 X^2+X X^3+X  X  0 X^2 X^3 X^3+X^2  X  X X^2+X X^3+X X^3+X^2+X X^3+X^2 X^3  X X^2 X^3+X^2+X X^3+X  0 X^2+X X^3 X^2  0 X^3+X^2 X^3+X^2+X X^2+X X^3 X^3+X  X  0 X^2+X X^3+X^2+X  X X^2 X^3+X  X X^3+X^2 X^2+X X^3 X^3+X  0  0 X^3+X X^2+X X^3+X^2+X

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+418x^87+280x^88+352x^89+144x^90+328x^91+158x^92+200x^93+32x^94+74x^95+22x^96+20x^97+8x^99+1x^100+4x^101+4x^103+1x^108+1x^136

The gray image is a linear code over GF(2) with n=720, k=11 and d=348.
This code was found by Heurico 1.16 in 432 seconds.